Measurement of CP violation in $B^0 \to J/\psi K^0_S$ and $B^0 \to \psi(2S) K^0_S$ decays

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A measurement is presented of decay-time-dependent CP violation in the decays $B^0 \to J/\psi K^0_S$ and $B^0 \to \psi(2S) K^0_S$, where the $J/\psi$ is reconstructed from two electrons and the $\psi(2S)$ from two muons. The analysis uses a sample of pp collision data recorded with the LHCb experiment at centre-of-mass energies of 7 and 8 TeV, corresponding to an integrated luminosity of 3 $fb^{−1}$. The CP -violation observables are measured to be $C(B^0 \to J/\psi K^0_S) = 0.12 \pm 0.07 \pm 0.02,$ $S(B^0 \to J/\psi K^0_S) = 0.83 \pm 0.08 \pm 0.01,$ $C(B^0 \to \psi(2S) K^0_S) = −0.05 \pm 0.10 \pm 0.01,$ $S(B^0 \to \psi(2S) K^0_S) = 0.84 \pm 0.10 \pm 0.01,$ where C describes CP violation in the direct decay, and S describes CP violation in the interference between the amplitudes for the direct decay and for the decay after $B^0 − \overline{B}^0$ oscillation. The first uncertainties are statistical and the second are systematic. The two sets of results are compatible with the previous LHCb measurement using $B^0 \to J/\psi K^0_S$ decays, where the $J/ψ$ meson was reconstructed from two muons. The averages of all three sets of LHCb results are $C(B^0 \to [c\overline{c}]K^0_S) = −0.017 \pm 0.029,$ $S(B^0 \to [c\overline{c}]K^0_S) = 0.760 \pm 0.034,$ under the assumption that higher-order contributions to the decay amplitudes are negligible. The uncertainties include statistical and systematic contributions.